That is, the appearance time of an edge is determined by their curvature. Nodes are forced to arise by the edges: once an edge appears, its endpoints appear too if they were not already there. Finally, a solid 2-dimensional triangle appears together with the last of its edges. The appearance time of triangles coincides with how they appear in the Vietoris-Rips complex, which is one of the most popular and easily computable ways of creating time filtrations in topological data analysis [1]}. Note too that whenever any 3-cycle is created, it is instantly filled with a face, so the 1-holes will be generated by cycles of length 4 or more. According to standard practice, the homology groups are calculated over the field \(\mathbb {Z}/2\) , which greatly reduces computation complexity and time.
